Recent content by Nat3

Homework Statement Sketch the following volume and find the area. Homework Equations 0 <= x <= 3, 0<= y <= 4, 0 <= z <= 5 The Attempt at a Solution The notation is confusing me. Is the equation simply representing a cuboid?

Good point! Oh snap! Thanks. I was having trouble visualizing this until you said "Imagine the inner radius is zero".. So the edges of the "rectangle" on the ends would be angled? I used the outer radius. Could I have used the average of the radii? Wow, thanks for such a detailed...

This actually isn't a homework problem -- I'm just trying to understand an example in my textbook. The example shows how to calculate the volume of a cylinder (maybe it's actually a shell, I'm not sure) using an integral, but it occurred to me that I should be able to simply "unwrap" the...

Like this? g(t)=5\bigg (\frac{180.2\angle 2.70^\circ}{1680.02\angle 0.29^\circ}\bigg) e^{j200\pi t}+5\bigg (\frac{180.2\angle -2.70^\circ}{1680.02\angle -0.29^\circ}\bigg) e^{-j200\pi t} g(t)=5(0.11\angle 2.41^\circ) e^{j200\pi t}+5(0.11\angle -2.41^\circ) e^{-j200\pi t}...

Did you by any chance mean: ##0.11\angle 2.41^\circ = Re(0.11 e^{j 2.41^\circ})##? Otherwise, I'm really confused :smile: Because: ##0.11\angle 2.41^\circ = 0.11\cos(\omega t + 2.41^\circ)## And: ##0.11 e^{j 2.41^\circ} = 0.11\cos(\omega t + 2.41^\circ) + j0.11\sin(\omega t + 2.41^\circ)##

Hmm... I've been trying to simplify it and am not sure how to proceed. I tried changing the polar portion to ##\cos## and using Euler's identity to change the exponentials to ##\cos## and ##\sin##, which gives: ##g(t) = 5[0.11\cos(\omega t + 2.41^\circ)[\cos(200\pi t) + j\sin(200\pi t)] +...

Does anyone know if what I did is correct? Operating under that assumption, I tried converting the rectangular coordinate complex numbers to polar form: g(t)=5\bigg (\frac{180.2\angle 2.70^\circ}{1680.02\angle 0.29^\circ}\bigg) e^{j200\pi t}+5\bigg (\frac{180.2\angle -2.70^\circ}{1680.02\angle...

Ah.. I'm not sure what I was thinking, lol :-) OK, so having this equation: g(t)=\int_{-\infty}^{\infty} 5[\delta(f+100)+\delta(f-100)]\bigg(\frac{180+j2\pi f*0.0135}{1680+j2\pi f*0.0135}\bigg) e^{j2\pi ft}dt When using the sifting/sampling property of the Dirac Delta function...

Homework Statement Take the inverse Fourier Transform of 5[\delta(f+100)+\delta(f-100)]\bigg(\frac{180+j2\pi f*0.0135}{1680+j2\pi f*0.0135}\bigg)Homework Equations g(t)=\int_{-\infty}^{\infty} G(f)e^{j2\pi ft}dt The Attempt at a Solution g(t)=\int_{-\infty}^{\infty}...

I plugged the integral into wolfram alpha and got the same answer as I posted in my original question: http://www.wolframalpha.com/input/?i=integrate+exp%28-alpha*t%29*exp%28-i*omega*t%29+from+0+to+infinity Unless I'm just forgetting basic integration rules, it seems like since the function is...

OK, looking at it again, I now realize that g(t) is a decaying exponential, starting at y = 1 and then going down to follow the x-axis. It's an even function because of the absolute value around t, so it's the same on both sides of the y-axis. Does that mean that I can just do the integration...

Thanks for your help! Ah, I guess since there's an absolute value around t, that actually make g(t) an even function? So g(t) is going to be the same equation and Fourier transform for t < 0 and t > 0? Shouldn't it be zero to infinity?

Homework Statement Calculate (from the definition, no tables allowed) the Fourier Transform of e^{-a*|t|}, where a > 0. Homework Equations Fourier Transform: G(f) = \int_{-\infty}^{\infty} g(t)e^{-j\omega t} dt The Attempt at a Solution I thought I'd break up the problem into the two cases...

Homework Statement Find the first three positive values of \lambda for which the problem: (1-x^2)y^n-2xy'+\lambda y = 0, \ y(0)=0, \ y(x) & y'(x) bounded on [-1, 1] has nontrivial solutions. Homework Equations When n is even: y_1(x) = 1 - \frac{n(n+1)}{2!}x^2 +...

Thanks again for your help. When n=3, the expression inside the Riemann sum is: \frac{8}{9\pi^2}\cos(\frac{3\pi}{4}t). In phasor form, I believe that is: \frac{8}{9\pi^2}\angle0\deg How can I find v_{out}(t)? In the S-Domain, I know that: H(s)=\frac{V_{out}(s)}{V_{in}(s)} But to...